Intro to finance chapter 6 questions

The interest rate that is most commonly quoted by a lender is referred to as which one of the following?

Annual percentage rate.

You are comparing two annuities that offer quarterly payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?

Annuity B has a smaller present value than annuity A.

Rosina plans on saving $2,000 a year and expects to earn an annual rate of 8.8 percent. How much will she have in her account at the end of 43 years?

FVA = $2,000 × {[(1 + .088)^43 - 1] / .088} = $831,532

An interest rate on a loan that is compounded monthly but expressed as an annual rate would be an example of which one of the following rates?

Effective annual rate.

Amortized loans must have which one of these characteristics?

Either equal or unequal principal payments over the life of the loan.

An ordinary annuity is best defined by which one of the following?

Equal payments paid at the end of regular intervals over a stated time period.

Waldo expects to receive the following payments: year 1 = $50,000; year 2 = $28,000; year 3 = $12,000. All of this money will be saved for his retirement. If he can earn an average annual return of 10.5 percent, how much will he have in his account 25 years after making the first deposit?

FV = $50,000 �1.10525 + $28,000 �1.10524 + $12,000 �1.10523 = $1,033,545

The government has imposed a fine on JJ's Place. The fine calls for annual payments of $60,000, $70,000, $75,000, and $50,000, respectively, over the next four years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including the investment earnings, to help the local community shelter. The government will earn 5.5 percent on the funds held. How much will the community shelter receive four years from today?

FV = $60,000 ×1.055^3 + $70,000 ×1.055^2 + $75,000 ×1.055 + $50,000 = $277,491

What is the future value of $1,400 a year for 35 years at 6 percent interest? Assume annual compounding.

FVA = $1,400 × {[(1 + .06)^35 - 1] / .06} = $156,009

Travis International has a one-time expense of $2.86 million that must be paid three years from now. Since the firm cannot raise that amount in one day, it wants to save an equal amount each month over the next three years to fund this expense. If the firm can earn 2.1 percent on its savings, how much must it save each month?

FVA = $2.86 million = C × ({[1 + (.021 / 12)]^(3 × 12) - 1} / (.021 / 12)) C = $77,037.69

You have been purchasing $9,000 worth of stock annually for the past 5 years and now have a portfolio valued at $45,881. What is your annual rate of return?

FVA = $45,881 = $9,000 × {[(1 + r)^5 - 1] / r} r = .97 percent

You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investments?

FVA = $73,262 = $250 × ({[1 + (r / 12)]^(13 × 12) - 1} / (r / 12)) r = 8.94%

Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal?

FVA Due = $1m = $75 × ({[1 + (r / 365)]^(17 × 365) - 1} / (r / 365))× [1 + (r / 365)] r = 8.09 percent

Your father helped you start saving $20 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?

FVA Due = $6,528.91 = $20 × ({[1 + (r / 12)]^(17 × 12) - 1} / (r / 12)) × [1 + (r / 12)] r = 5.15 percent

Racing Engines wants to save $750,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal?

FVA Due = $750,000 = C × ({[1 + (.0475 / 4)^](4 × 4) - 1} / (.0475 / 4)) × [1 + (.0475 / 4)] C = $42,337.00

Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?

FVA Due = ($250 + 125) × {[(1 + .005)^(25 × 12) - 1] / .005} × 1.005 = $261,172

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $16,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

GAPV = $16,500 �({1 - [(1 + .05) / (1 + .075)]^20} / (.075 - .05)) = $247,750

You just settled an insurance claim. The settlement calls for increasing payments over a five-year period. The first payment will be paid one year from now in the amount of $7,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments?

GAPV = $7,000 ×({1 - [(1 + .035) / (1 + .065)]^5} / (.065 - .035)) = $31,063.79

You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate.

Option B has a higher present value at time zero.

Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses. The account pays .45 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next four years?

PV = $1,700 ×({1 - [1 / (1 + .0045)^(4 ×4)]} / .0045) = $26,187.10

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 13.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday Vacations?

PV = $187,000 / 1.135 + $220,000 / 1.135^2 + $245,000 / 1.135^3 = $503,098

You are considering two savings options. Both options offer a rate of return of 11 percent. The first option is to save $2,500, $1,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

PV = $2,500 / 1.11 + $1,500 / 1.11^2 + $3,000 / 1.11^3 = $5,663.26

You just signed a consulting contract that will pay you $38,000, $52,000, and $85,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a discount rate of 10.5?

PV = $38,000 / 1.105 + $52,000 / 1.105^2 + $85,000 / 1.105^3 = $139,975

You want to start your own consulting business and believe it could produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $450,000. At a 14 percent discount rate, what is this business idea worth today?

PV = $5,600 / 1.14 + $48,200 / 1.14^2 + ($125,000 + 450,000) / 1.14^3 = $430,109

An insurance annuity offers to pay you $1,000 per quarter for 20 years. If you want to earn a rate of return of 6.5 percent, what is the most you are willing to pay as a lump sum today to buy this annuity?

PVA = $1,000 × [(1 - {1 / [1 + (.065 / 4)]^(20 × 4)}) / (.065 / 4)] = $44,591.11

You just won the grand prize in a national writing contest! As your prize, you will receive $1,000 a month for 10 years. If you can earn 7 percent on your money, what is this prize worth to you today?

PVA = $1,000 × [(1 - {1 / [1 + (.07 / 12)]^(10 × 12)}) / (.07 / 12)] = $86,126.35

As the beneficiary of a life insurance policy, you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. If you can earn 6 percent on your money, which option should you take and why?

PVA = $1,400 × [(1 - {1 / [1 + (.06 / 12)]^(20 × 12)}) / (.06 / 12)] = $195,413

Nadine is retiring today at age 66 and expects to live to age 82. She has $136,000 in her retirement savings account. She is somewhat conservative with her money and expects to earn 6 percent during her retirement years. How much can she withdraw from her retirement savings each month if she plans to spend her last penny on the morning of her death?

PVA = $136,000 = C × [(1 - {1 / [1 + (.06 / 12)]^(16 × 12)}) / (.06 / 12)] C = $1,103.56

Your grandmother is gifting you $150 a month for four years while you attend college to earn your bachelor's degree. At a 4.8 percent discount rate, what are these payments worth to you on the day you enter college?

PVA = $150 × [(1 - {1 / [1 + (.048 / 12)]^(4 × 12)}) / (.048 / 12)] = $6,539.14

You are borrowing $21,800 to buy a car. The terms of the loan call for monthly payments for five years at 8.25 percent interest. What is the amount of each payment?

PVA = $21,800 = C × [(1 - {1 / [1 + (.0825 / 12)]^(5 ×12)}) / (.0825 / 12)] C = $444.64

The Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $25,000 and only one company will loan to them. The terms of the loan call for weekly payments of $500 at a weekly interest rate of .45%. What is the loan term?

PVA = $25,000 = $500 × ({1 - [1 / (1 + .0045)^t]} / .0045) t = 56.77 weeks

You estimate that you will owe $39,950 in student loans by the time you graduate. The interest rate is 3.75 percent. If you want to have this debt paid in full within 10 years, how much must you pay each month?

PVA = $39,950 = C × [(1 - {1 / [1 + (.0375 / 12)]^(10 × 12)}) / (.0375 / 12)] C = $399.74

Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 a month for the next 20 years. What is the rate of return on this investment?

PVA = $50,000 = $250 × [(1 - {1 / [1 + (r / 12)]^(20 × 12)}) / (r / 12)] r = 1.88 percent

Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120?

PVA = $6,200 = $120 × [(1 - {1 / [1 + (.149 / 12)]^t }) / (.149 / 12)] t = 83.14 months, or 6.93 years

Your employer contributes $60 a week to your retirement plan. Assume you work for your employer for another 20 years and the applicable discount rate is 9 percent. Given these assumptions, what is this employee benefit worth to you today?

PVA = $60 × [(1 - {1 / [1 + (.09 / 52)]^(20 × 52)}) / (.09 / 52)] = $28,927.38

You are buying a pre-owned car today at a price of $8,500. You are paying $300 down in cash and financing the balance for 36 months at 7.75 percent. What is the amount of each monthly loan payment?

PVA = ($8,500 - 300) = C × [(1 - {1 / [1 + (.0775 / 12)]^36}) / (.0775 / 12)] C = $256.01

Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease?

PVA Due = $190 × [(1 - {1 / [1 + (.065 / 12)]^36}) / (.065 / 12)] × [1 + (.065 / 12)] = $6,232.80

You just purchased an annuity that will pay you $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?

PVA Due = $24,000 × ({1 - [1 / (1 + .085)^25]} / .085)× (1 + .085) = $266,498

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $30 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much money are you borrowing?

PVA Due = $30 × ({1 - [1 / (1 + .02)^6]} / .02) × (1 + .02) = $171.40

Which one of the following statements is correct given the following two sets of project cash flows? Assume a positive discount rate. Project A Project B Year 1 $4,000 $2,000 Year 2 3,000 3,000 Year 3 0 2,000 Year 4 3,000 3,000

Project B is worth less today than Project A.